For air mass in meteorology, see air mass.

The airmass in astronomy quantifies the path length that the light from a celestial source must travel through the Earth's atmosphere to get to the observatory, relative to that for a source at the zenith.

When the zenith distance is less than 60 degrees, a good approximation is given by assuming a plane parallel atmosphere. In this case, the airmass is simply the secant of the zenith distance, which is often denoted "sec(zen)".

By definition, a source at the zenith has an airmass of 1. A source at a zenith distance of 60 degrees (i.e. at an altitude = 90 - zenith distance = 30 degrees) has an airmass of 2.

A corrected formula is used for observations near the horizon:

$A\; =\backslash sec(zen)\; (1\; -\; 0.0012\; \backslash cdot\; \backslash sec^2(zen))$

where:

$zen$ denotes the distance to the zenith

This multiplies $\backslash sec(zen)$ times a correction term which is usually very close to 1 (0.9988 in the zenith) and grows as the distance increases. Unfortunately this ends in an asymptotic behavior at 90 degrees where the airmass decreases very fast, making this expression unsuitable for observations at really small distances from the horizon.

For observations even closer to the horizon, a second expression might be useful:

$A=\; \backslash frac\{1\}\; \{\; \backslash cos(zen)\; +\; 0.50572(96.07995\; -\; zen)^\{-1.6364\}\}$

This formula works for degrees and most software do the calculations in radians, so you have to use radians for the term inside the cosine but leave the other term in degrees.

External links

A downloadable airmass calculator, written in C (the source code describes the theory in detail)

Spherical astronomy